NIST Technical Note 1337: Characterization of Clocks and Oscillators

of the wide range of measurement situations which might be encountered. However, it can serveas a starting point for the decision-making process.Section A6 contains some new material which should be helpful in understanding therelationship between the Allan variance and the modified Allan variance. Since these ideas areunpublished, we include them here rather than with the papers on those topics. This section isfollowed by a reading list with references to major articles and books which can be used assupplementary resources. Because some of the papers include extensive reference lists, we havelimited our list to works which are either very comprehensive or only recently published. Particularlyextensive reference lists are included with papers 8.1, B.2, C.l, C.3, D.l, and D.2.Since notation and definitions have changed over the period bridged by these papers, wehave highlighted problem areas on the papers with an asterisk (*). A note directs the reader tothe Appendix where the particular problem is discussed. We have also used this device tohighlight inconsistencies and the usual typographic and other errors which creep into the literature.The page numbers of the original publications are retained, but we have also used acontinuous page numbering to simplify location of items in the volume.The topical index on page xi organizes much of the material in the papers under a fewkey subject headings. This index provides a shortcut to locating material on a particular topic.A.2 COMMENTS ON INTRODUCTORY AND TUTORIAL PAPERSPaper B.l in this section, by Howe, Allan, and Barnes, was originally prepared andpresented as a tutorial paper and has been used with success as an introductory paper in ourannual Time and Frequency Seminar. This paper is now 9 years old, so there are a substantialnumber of notes which relate to updates in notation. The paper is nevertheless highly readableand introduces many of the key measurement methods, providing circuit diagrams with enoughspecific detail to be useful in real laboratory situations. Furthermore, it includes discussion andexamples on handling of data which are useful for practical application of the concepts. Thepaper presents a particularly useful discussion of the pitfalls encountered in digitizing data, aproblem which is often overlooked.The second paper (B.2) by Stein is more advanced and those familiar with the generalconcepts may find it a better starting point. This and other papers in this collection cite earlierIEEE recommendations on measures of frequency stability and, while much of this has notchanged, there is a new IEEE standard (paper C.l). In general, the reader should consult theoverview and papers of section C if there is any question concerning definitions or terminology.Paper B.2 is quite comprehensive, introducing topics (not covered in paper B.l) such as themodified Allan variance, the delay-line-phase-noise-measurement system, and the use of frequencysynthesis to reach frequencies far from normally available reference frequencies.The materials in papers B.l and B.2, aside from differences in level of presentation, areorganized in quite different ways. The Howe-Allan-Barnes paper goes directly to the measurementconcepts and then describes the means for analyzing the output data and understanding theconfidence of the measurements. On the other hand, the Stein paper carefully lays out thetheoretical background needed to analyze the data before introducing the measurement concepts.Both papers cover time-domain and frequency-domain measurements.Paper B.3 by Allan reviews the concepts of the two-sample or Allan variance and themodified Allan variance showing how classical statistical methods fail to usefully describe thetime-domain performance of good oscillators. The Allan variance concept is also introduced inTN-2